Hostname: page-component-7b7567c8c-jswmv Total loading time: 0 Render date: 2026-11-15T21:14:28.613Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditional Sequence Entropy and Mild Mixing Extensions

Published online by Cambridge University Press:  20 November 2018

Qing Zhang
Qing Zhang*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

For a measure preserving system (X, ℬ, μ, T) with a factor (Y, C, v, T) and an infinite sequence {tn}, one can define conditional sequence entropy. We present two theorems which characterize rigid and mildly mixing extensions by conditional sequence entropy. Properties of IP-systems are used to prove our main theorems.

Keywords

28D20

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 2 , 01 April 1993, pp. 429 - 448
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Furstenberg, H., IP-systems in Ergodic Theory, Contemporary Mathematics, Conference in Modern Analysis and Prob. 26(1984), 131–148.Google Scholar
2. Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, N.J., 1981.Google Scholar
3. Furstenberg, H. and Katznelson, Y., An Ergodic Szemeredi Theorem for IP-systems and Combinatorial Theory, J. d'Analyse Math. 45(1985), 117–169.Google Scholar
4. Furstenberg, H. and Weiss, B., Topological Dynamics and Combinatorial Number Theory, J. d'Analyse Math. 34(1978), 161–185.Google Scholar
5. Hindman, N., Finite Sums from Sequence within One Cell of a Partition ofN, J.Combinatorial Theory (A) 17(1974), 1–11.Google Scholar
6. Hulse, P., Sequence Entropy Relative to an Invariant a-algebra, J. London Math. Soc. (2) 33(1986), 59–72.Google Scholar
7. Kushnirenko, A.G., On Metric Invariants of Entropy Type, Russian Math. Surveys (5) 22(1967), 53–61.Google Scholar
8. Rokhlin, V.A., Lectures on the Entropy Theory of Transformations with Invariant Measure, Russian Math. Surveys (5) 22(1967), 1–52.Google Scholar
9. Saleski, A., Sequence Entropy and Mixing, J. Math. Anal. Appl. 60(1977), 58–66.Google Scholar
10. Walters, P., An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982.Google Scholar
11. Yosida, K., Functional Analysis, Springer-Verlag, New York, 1968.Google Scholar
12. Zhang, Q., Sequence Entropy and Mild Mixing, Can. J. Math. (1) 44(1992), 215–224.Google Scholar
13. Zimmer, R.J., Extensions ofergodic group actions, Illinois J. Math. 20(1976), 373–409.Google Scholar
14. Zimmer, R.J., Ergodic actions with generalized discrete spectrum, Illinois J. Math. 20(1976), 555-588Google Scholar